In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth order Riemann-Lovelock tensor is determined by its traces in dimensions 2k ≤ D < 4k. In...

In this work we develop a perturbative formalism for the treatment of Lovelock theories of gravity. We consider in detail D-dimensional models in Lovelock gravity with an induced metric given by the product of the metrics of two maximally symmetric spaces. We first explicitly obtain the Lovelock action, Hamiltonian constraint, gravitational momenta, and dynamical equations for this type of mini...

Starting from the SO(2, 2n) Chern–Simons form in (2n + 1) dimensions we calculate the variation of conserved quantities in Lovelock gravity and Lovelock–Maxwell gravity through the covariant formalism developed in [23]. Despite the technical complexity of the Lovelock Lagrangian we obtain a remarkably simple expression for the variation of the charges ensuing from the diffeomorphism covariance ...

Colliding and intersecting thin membranes of matter are studied in the Lovelock higher order curvature theory of gravity. We restrict the study to constant curvature membranes in constant curvature AdS and dS background and consider their general intersections. This illustrates some key features which make the higher Lovelock theory different to the Einstein gravity. Lovelock terms couple hyper...

The Komar integral relation of Einstein gravity is generalized to Lovelock theories of gravity. This includes, in particular, a new boundary integral for the Komar mass in Einstein gravity with a nonzero cosmological constant, which has a finite result for asymptotically AdS black holes, without the need for an infinite background subtraction. Explicit computations of the Komar mass are given f...

We study quasistationary physical process for black holes within the context of Lanczos-Lovelock gravity. We show that the Wald entropy of the stationary black holes in Lanczos-Lovelock gravity monotonically increases for quasistationary physical processes in which the horizon is perturbed by the accretion of positive energy matter and the black hole ultimately settles down to a stationary stat...

We study holographic implications of Lovelock gravities in AdS spacetimes. For a generic Lovelock gravity in arbitrary spacetime dimensions we formulate the existence condition of asymptotically AdS black holes. We consider small fluctuations around these black holes and determine the constraint on Lovelock parameters by demanding causality of the boundary theory. For the case of cubic Lovelock...

It is well known that black strings and branes may be constructed in pure Einstein gravity simply by adding flat directions to a vacuum black hole solution. A similar construction holds in the presence of a cosmological constant. While these constructions fail in general Lovelock theories, we show that they carry over straightforwardly within a class of Lovelock gravity theories that have (loca...

In Einstein’s gravity, the entropy of horizons is proportional to their area. Several arguments given in the literature suggest that, in this context, both area and entropy should be quantized with an equallyspaced spectrum for large quantum numbers. But in more general theories (like, for example, in the black hole solutions of Gauss-Bonnet or Lanczos-Lovelock gravity) the horizon entropy is n...

A four-dimensional regularization of Lovelock–Lanczos gravity up to an arbitrary curvature order is considered. We show that terms can provide a non-trivial contribution the Einstein field equations in four dimensions, for spherically symmetric and Friedmann–Lemaître–Robertson–Walker spacetimes, as well at first perturbation theory around (anti) de Sitter vacua. will discuss cosmological black ...